1. **State the problem:** Solve the inequality $\frac{x}{2} + 1 \leq 5$. 2. **Formula and rules:** To solve inequalities, we isolate the variable on one side. Remember, when multiplying or dividing by a negative number, the inequality sign reverses. 3. **Step 1:** Subtract 1 from both sides: $$\frac{x}{2} + 1 - 1 \leq 5 - 1$$ $$\frac{x}{2} \leq 4$$ 4. **Step 2:** Multiply both sides by 2 to solve for $x$: $$2 \times \frac{x}{2} \leq 4 \times 2$$ $$x \leq 8$$ 5. **Final answer:** The solution to the inequality is: $$x \leq 8$$ This means $x$ can be any number less than or equal to 8.